## Littlewood complexes for symmetric groups

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- by Christopher Ryba
- Represent. Theory
**25**(2021), 594-605 - DOI: https://doi.org/10.1090/ert/575
- Published electronically: July 13, 2021
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## Abstract:

We construct a complex $\mathcal {L}_\bullet ^\lambda$ resolving the irreducible representations $\mathcal {S}^{\lambda [n]}$ of the symmetric groups $S_n$ by representations restricted from $GL_n(k)$. This construction lifts to $\mathrm {Rep}(S_\infty )$, where it yields injective resolutions of simple objects. It categorifies stable Specht polynomials, and allows us to understand evaluations of these polynomials for all $n$.## References

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## Bibliographic Information

**Christopher Ryba**- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 1317998
- ORCID: 0000-0002-8114-8263
- Email: ryba@math.berkeley.edu
- Received by editor(s): May 28, 2020
- Received by editor(s) in revised form: March 2, 2021
- Published electronically: July 13, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory
**25**(2021), 594-605 - MSC (2020): Primary 20C30, 20C32
- DOI: https://doi.org/10.1090/ert/575
- MathSciNet review: 4296002